Average Error: 0.0 → 0
Time: 1.6m
Precision: 64
\[0.0 \le x \le 2\]
\[x + x \cdot x\]
↓
\[\mathsf{fma}\left(x, x, x\right)\]
x + x \cdot x
↓
\mathsf{fma}\left(x, x, x\right)
double f(double x) {
        double r3935726 = x;
        double r3935727 = r3935726 * r3935726;
        double r3935728 = r3935726 + r3935727;
        return r3935728;
}
↓
double f(double x) {
        double r3935729 = x;
        double r3935730 = fma(r3935729, r3935729, r3935729);
        return r3935730;
}

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0
\[\left(1 + x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, x\right)\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

  :herbie-target
  (* (+ 1.0 x) x)

  (+ x (* x x)))